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|Title:||On the Convergence of an Implicit Iteration Scheme for a Finite Family of Asymptotically Nonexpansive Mappings in Banach Spaces|
Choudhury, Binayak S.
|Keywords:||Implicit iteration process with errors|
asymptotically nonexpansive mapping
uniformly convex Banach space
common fixed point
Condition (B )
|Publisher:||Vidyasagar University , Midnapore , West-Bengal , India|
|Series/Report no.:||Journal of Physical Science;Vol 12 |
|Abstract:||In this paper we define a new implicit iterative process with errors in a real Banach space and establish a necessary and sufficient condition for the strong convergence of the iteration to a common fixed point for the case of a finite family of asymptotically nonexpansive mappings in a arbitrary real Banach space. Also we study the weak and strong convergence results of this implicit iterative scheme for the same family of mappings in the setting of a uniformly convex Banach space. Our results extend and generalize a number of existing results.|
|Appears in Collections:||Journal of Physical Sciences Vol.12 |
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